Embodiments of the invention achieve a very high success rate in multilayer peer-to-peer connection across firewalls and network address translators (NATs) using a single port on the local host. In one embodiment, a system of providing peer-to-peer connection comprises a plurality of host devices disposed behind corresponding NATs; and a plurality of STUN servers. Each host device includes a first socket bound to a first private port and a second socket bound to a second private port. Each host device sends a first STUN packet through the first socket to a first STUN server and a second group of STUN packets through the second socket to the STUN servers via public ports of the corresponding NAT. The STUN servers identify the public port numbers of the public ports. Each host device is configured to calculate a predicted public port number of the corresponding NAT for the second socket, based on the public port numbers of the public ports for the first socket and the second socket, the predicted public port number to be used for peer-to-peer connection between the second socket of the host device and other host devices.